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Effective roughness and displacement height over forested areas, via reduced-dimension CFD

Sogachev, Andrey; Cavar, Dalibor; Kelly, Mark C.; Bechmann, Andreas

Publication date:2017

Document VersionPublisher's PDF, also known as Version of record

Link back to DTU Orbit

Citation (APA):Sogachev, A., Cavar, D., Kelly, M. C., & Bechmann, A. (2017). Effective roughness and displacement heightover forested areas, via reduced-dimension CFD. DTU Wind Energy E, Vol.. 0161

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Effective roughness and displacement height over forested areas, via reduced-dimension CFD

Andrey Sogachev, Dalibor Cavar, Mark Kelly, Andreas

Bechmann

DTU Wind Energy E-0161

December 2017

Authors: Andrey Sogachev, Dalibor Cavar, Mark Kelly, Andreas Bechmann

Title: Effective roughness and displacement height over forested areas, via

reduced-dimension CFD

Department: DTU Wind Energy

DTU Wind Energy E-0161

December 2017

Summary (max 2000 characters):

While extensive field campaigns as well as modern remote sensing methods

based on airborne laser scans allow obtaining of detailed information about

forest canopy structure, there is still a great need for simple and consistent

description of vegetation roughness, as its parametrization differs

significantly from one flow model to the other (e.g. CFD, mesoscale and

linearized models). Here, we present a method to facilitate use of forest data,

having an arbitrary level of detail, in flow models employing different

types or levels of canopy drag-force prescription.

ISBN 978-87-93549-29-6

Pages: 35

Figures: 22

References: 36

Technical University of Denmark Department of Wind Energy Frederiksborgvej 399 Building 118 4000 Roskilde Denmark Telephone +4521331197 anso@dtu.dk www.vindenergi.dtu.dk

Content

Summary ........................................................................................................................................ 4 

1. Introduction ................................................................................................................................. 5 

2. Derivation and parameterization of PAD .................................................................................... 5 

2.1 Statistical approach ..................................................................................................................... 5 

2.2 Empirical method ........................................................................................................................ 6 

3. Translating PAD to effective roughness and displacement height ............................................ 8 

3.1 Estimation of effective roughness ............................................................................................... 8 

3.2 Derivation of displacement height and aerodynamic roughness ................................................. 8 

3.3 Data filtering ................................................................................................................................ 9 

4. Numerical experiments ............................................................................................................. 10 

5. Case study................................................................................................................................ 11 

6. Results ...................................................................................................................................... 12 

6.1 Forest height, PAI, PAD and effective roughness around Østerild test station ......................... 12 

6.2 Effect of different levels of canopy drag-force prescription on flow modelling ........................... 18 

6.2.1 Initialization ................................................................................................................ 18 

6.2.2 Wind speed simulations ............................................................................................. 19 

6.2.3 TKE simulations ......................................................................................................... 24 

7. Discussion ................................................................................................................................ 28 

8. Conclusions .............................................................................................................................. 30 

References ................................................................................................................................... 31 

Appendix A Allometric relationships for Scots Pine .................................................................... 33 

4

Summary

While extensive field campaigns as well as modern remote sensing methods based on airborne

laser scans allow obtaining of detailed information about forest canopy structure, there is still a

great need for simple and consistent description of vegetation roughness, as its parametrization

differs significantly from one flow model to the other (e.g. CFD, mesoscale and linearized

models). Here, we present a method to facilitate use of forest data, having an arbitrary level of

detail, in flow models employing different types or levels of canopy drag-force prescription.

5

1. Introduction

The lack of accurate information about forest canopy structure currently limits the accuracy of

numerical predictions of the wind field over forested terrain. While forest has commonly been

represented via roughness length and displacement height in wind models, these parameters

have often been defined in subjective ways without relation to the actual forest structure at a

given site (e.g. Raupach, 1994). Alternatively, the canopy structure in Computational Fluid

Dynamics (CFD) can be specified directly through the Plant Area Density (PAD) for each grid

volume in a three-dimensional (3D) model domain. Advanced CFD models capable of

incorporating (distributed) local drag forces have attained widespread use in wind energy, so

proper application of PAD measurements becomes highly important. Here we consider methods

to parameterize the PAD description including translation into roughness aiming to facilitate use

of such forest data in flow models with different types or levels of canopy drag-force prescription

(e.g. CFD, mesoscale and linearized models); it also allows comparison with known theory,

measurements, and commonly used parameters in forest-flow modelling.

2. Derivation and parameterization of PAD

2.1 Statistical approach

The information about PAD can be derived by different methods. In traditional forestry, most

structural properties — like tree height, crown width, crown length, etc. — have been related by

allometric relationships to an easily measurable primary variable. In most cases this variable is

the Diameter-at-Breast-Height (DBH) i.e., the diameter of the tree trunk at a height of 1.37 m

above the ground. Based on this parameter h (tree height) and PAI (plant area index) for

different spices can be estimated (see Widlowski et al., 2003; Picard et al., 2012). Plant Area

Density is related to the Plant Area Index (PAI) by

0

PAI PAD( )h

z dz , (1)

where z is the height above the ground.

Field experiments also provide detail information about tree properties including vertical foliage

distribution (e.g. Ross, 1981; Breuer et al., 2003). Another possibility to derive vegetation height

is to use digital elevation map. Considering the difference between topography and elevation

data one can estimate the height of object over ground level, including the vegetation height.

Based on this information some robust assumptions about the PAD can be done (Mann et al.,

2010; Sogachev et al., 2015). Nowadays airborne laser scans are becoming a more popular

method of getting the information about vegetation properties. Methods allowing to calculate

highly heterogeneous and realistic PAD from LiDAR scan data are developed (Lefsky et al.,

1999; Solberg et al., 2006; Morsdorf et al, 2006; Richardson et al., 2009; Boudreault et al.,

2015). While such PAD data is in principle applicable to CFD models handling high-resolution

6

input, such data must presently be processed in order to be usable for general wind flow

modelling.

To use detailed information about forest in the model, one usually apply a statistical approach in

an attempt to order frontal density data into a number of land-use classes, before describing the

mean properties within each. Accordingly, based on forest height information the vegetation is

subdivided in classes. After that each height class is used to derive the PAI value. Statistical

analysis of LiDAR scan data can easily provide mean values for each height class as well as

the mean shape of foliage. If LiDAR scan data is unavailable, the PAI and PAD can be

estimated using above mentioned allometric relationships of traditional forestry.

2.2 Empirical method

Independent of the method for derivation of PAD and in order to facilitate its usage in the

models, one usually utilize the two well-known empirical methods of description of normalized

PAD profiles through a number of simple parameters: one based on the beta-distribution

(Meyers and Paw U ,1986), and one suggested by Lalic and Michailovic (2004). Both methods

consider mean values of h and zm (the height where maximum plant area density PADm occurs)

in each class as key parameters in the definition of the vertical plant structure. The beta

probability density function, formulated as follows:

1

0

1111

11PAI)(PAD

hdz

h

z

h

z

h

z

h

zz

, (2)

has been used previously to represent profiles of plant area density (e.g. Meyers and Paw U,

1986; Markkanen et al., 2003) or source distribution (e.g. Van Den Hurk and McNaughton,

1995) inside the canopy. The mode of a beta-distributed random variable with parameters α, β >

1 is the most likely value of the distribution (corresponding to the peak in the PDF) and is given

by:

2

1

M . (3)

Thus, using (2) with M = zm/h, one can easily examine the effect of different canopy densities

and structures on the scalar and flow dynamics. Two parameters (α, β) determine the shape of

the distribution. For example, when α > β the maximum value occurs at z/h > 0.5, corresponding

to a region of maximum foliage (or a source) concentrated in the upper part of the canopy. For

given zm/h and β value we can estimate α from:

1

112

h

z

h

z mm . (4)

Thus to find α and β for a given height class, we have to iteratively solve the set of equations (2)

and (4) until the best correspondence between PAD(zm) and PADm is obtained.

7

Applying a mathematical procedure established by Plank (see Lalic and Michailovic (2004) and

references therein), Lalic and Michailovic (2004) also found that PAD(z) can approximately be

described by a function of the following form:

zh

zh

zh

zhz mm 1expPAD)(PAD m

, (5)

where

.5.0

00.6

hzz

zz

m

m

This function was validated against plant area density observations from eight sites located in

four different types of forest, covering a broad range of mean values of PAI between 2 and 18.

Figure 1 shows that two empirical methods result in different vertical plant area profiles even for

vegetation with the same PAI and same location of maximum foliage. The difference becomes

small for zm/h higher than 0.8.

Figure 1. Normalized vertical profiles of foliage density for different forest architectures

described according to Eq. (2) (solid lines) with varied α and fixed β at β = 3 and according to

Eq. (5) (dashed lines) with zm/h derived from Eq.(4) for α and β used in Eq. (2).

8

3. Translating PAD to effective roughness and displacement height

3.1 Estimation of effective roughness

Here we present a novel approach using the SCADIS solver — an Atmospheric Boundary Layer

(ABL) code capable of simulating canopy flows (Sogachev et al., 2002; Sogachev, 2009), in

order to estimate the effective aerodynamic roughness length, z0,eff — thereby describing each

land-use class with a single parameter. SCADIS provides steady-state profiles of velocity

components, turbulent kinetic energy, dissipation rate and the mean momentum flux for

specified geostrophic wind, G, latitude and a predefined canopy drag. Thus, the “geostrophic

drag law” (e.g., Blackadar and Tennekes, 1968) is implicitly applied, which, combined with

Rossby number similarity theory, gives the following geostrophic wind in the neutral, barotropic

boundary layer:

21

2

2

,0

** ln

BA

zf

uuG

eff. (6)

Thus

AB

u

G

f

uz eff

21

2

2

*

*,0 exp

. (7)

In equations (6) and (7) κ is the von Kármán constant (usually accepted to be 0.4), f is the Coriolis parameter, u

* is the friction velocity at the ‘virtual’ surface (generally the mean tree top

height). The geostrophic component coefficients {A, B} have historically been established

empirically via ABL measurements (Melgarejo and Deardorff, 1974; Clarke and Hess, 1974).

Our calculations used A = 1.8 as in Troen and Peterson (1989) and wind energy practice

(roughly equal to the mean of values found in literature). The value B = 6.4 is fitted to match

solutions of SCADIS with drag forces and z0,eff, and is slightly higher than the mean value of B

given by Troen and Peterson (1989) (see Section 7 for discussion). In calculations, G is taken

as 10 m s-1 and f is specified in accordance to the location of the test site (see below).

3.2 Derivation of displacement height and aerodynamic roughness

Use of the z0,eff parameter allows us to predict airflow over a surface covered by the vegetation

using a flow model, without explicitly resolving the canopy drag. In order to describe the mean

wind U above a surface covered by a vegetative canopy, using similarity theory, a displacement

height (d) is needed in addition to the aerodynamic roughness length (z0):

9

0

* ln)(z

dzuzU

. (8)

Note that z0 is not the same as z0,eff. Expression (8) implies that the flow should be “deflected”

upwards in such a way that the mean flow properties above a vegetative canopy (forest),

beginning roughly from a height d within the forest, are similar to those above the open flat

ground. There are several approaches to estimating d and z0 from only forest parameters, i.e.

the tree height and PAI (Raupach, 1992; 1994). They are quite simple to use, but lack validation

against real field conditions. These approaches do not account for the vertical vegetation

structure either and suffer from a need to specify several fitting parameters. Therefore, we again

apply SCADIS simulations to estimate d and z0, following Sogachev and Kelly (2016):

hh

dzdU

uhd

/*

, (9)

hu

hUdhz

*0

)(exp)(

, (10)

where subscript h refers to the canopy-top values. Although expression (8), as we will see

below, allows only for estimation of U in the shallow layer above the canopy, we estimate d and

z0 as a unique set of parameters for each of the specified classes.

3.3 Data filtering

Specified only in the 2D horizontal space, the parameters z0,eff, d and z0 can be smoothed or

aggregated for potential application. To do that, we use a bilateral filter, which is a non-linear

edge-preserving and noise-reducing smoothing operator, originally introduced by Tomasi and

Manduchi (1998) for images. The intensity value of each pixel in an image, g(i, j), is replaced by

a weighted average of intensity values from nearby pixels, φ(l, m),

ml

ml

mlji

mljimljig

,

,

,,,

,,,,),(

. (11)

This weight can be based on a Gaussian distribution. Also, the weight depends not only on

Euclidean distance of pixels (a spatial or domain kernel),

2

22

2exp),,,(

s

mjlimljis

, (12)

but also on the radiometric differences (e.g. range differences, such as color intensity, depth

distance or as in our case z0,eff, d and z0 — a data-dependent range kernel)

10

2

2

2

),(),(exp),,,(

r

mljimljir

. (13)

Multiplying expressions (12) and (13) one obtains the data-dependent bilateral weight-function:

22 2

2 2

( , ) ( , )( , , , ) exp

2 2s r

i j l mi l j mi j l m

. (14)

As the range parameter σr increases, the bilateral filter gradually approaches the Gaussian

convolution more closely, because the range Gaussian (r) widens and flattens, becoming nearly

constant over the intensity interval of the ‘image’ (here aerodynamic properties of canopy/class

area). As the spatial parameter σs increases, most of the “minor” features get smoothened out.

4. Numerical experiments

As mentioned above, ABL model SCADIS (Sogachev et al., 2002; Sogachev, 2009) in its one-

dimensional mode is a basic tool for translating the PAD into the effective roughness and

displacement height. SCADIS in its two or three-dimensional mode also allows airflow

estimation over complex terrain. However, the model is designed for a single processor use and

cannot be utilized on a massive computing scale, needed in the wind industry. Another DTU

Wind Energy’s in-house CFD solver — EllipSys3D (e.g. Michelsen, 1992; Sørensen, 2003) have

however been designed for massive parallel computing. Both models apply the two-equation

closure approach based on coupled transport equations for the turbulent kinetic energy (TKE),

k, and a supplementary length-scale determining variable φ ( φ = ε, ω, where ε is the dissipation

rate of turbulent kinetic energy, k, and ω = ε/k is the specific dissipation) (e.g. Pope, 2000). In

the present work both models will be used for test of the method: SCADIS only with k - ω

turbulent closure and EllypSys3D with k - ω and k - ε closures.

The SCADIS solution is based on a finite difference numerical approach, while EllipSys3D

utilizes a finite volume numerical method. To make results comparable, we used an upwind

discretization scheme for the advection term in EllipSys3D, as this is the only option in SCADIS.

An initial condition for wind speed was also identical and specified for flat plain terrain with

aerodynamic roughness of 0.03 m, with western geostrophic wind of G = 10 m s-1, at the upper

border of the modelling domain (2 km in SCADIS and 5 km in EllipSys3D).

Calculations were conducted first with full description of canopy drag (for the method see

Sogachev et al., 2012; 2015) and after that with effective roughness replacing the vegetation.

11

5. Case study

The Østerild National Test Centre for Large Wind Turbines is located on a coastal plain, in

northern Jutland, Denmark (http://www.vindenergi.dtu.dk/english/test-centers/oesterild). Figure

2 shows digital topography map (DTM) (Fig. 2a) and digital surface map (DSM) (Fig.2b) from a

national topography database (DHM – Danmarks Højdemodel,

http://download.kortforsyningen.dk) before the test centre was build and part of forest

surrounding it was cut. The terrain is flat, except for a small hill in the southwest direction and

some sand dunes to the north. The elevations of the test area range from approximately 12 to

14 m ASL. The surroundings are dominated by the North Sea, which is approximately 4 km to

the north and 20 km to the west. There is also the Limfjord entrance about 6 km to the

southeast. The site has grasslands, and forests in the southern half of the test site with canopy

heights between 10 m and 20 m. The original data set provides the horizontal resolution as

1.6 m. To demonstrate method and to speed-up data processing we use here the resolution of

16 m.

Figure 2. DTM (a) and DSM (b) of Østerild area. White line contours the area of the Østerild

National Test Centre.

12

6. Results

6.1 Forest height, PAI, PAD and effective roughness around Østerild test station

The base for derivation of effective roughness over Østerild site is the height of objects over the

ground (Fig.3), which is derived as difference between DSM and DTM datasets. There are few

artificial objects in this area, thus the assumption that difference between DSM and DTM is the

horizontal distribution of the tree height was utilized. In earlier works the vegetation, for

simplicity, was ranked in seven height classes with assumed constant PAI and with PAD given

by Eq. (2) with a priori assumption of α and β parameters. Such land use classes were used in

modelling for preliminary assessments of landscape on airflow over expected position of the

Test Centre in Mann et al. (2010) and to test and validate the performance of EllipSys3D model

after implementation of canopy parameterization (Sogachev at. al. 2015).

Figure 3. Map of objects over ground surface.

In the present work plant heights were binned (rounding to the nearest integer value of h), and

assigned to a class N (henceforth N = h). PAI and PAD for each class (or rounded height) were

derived using allometric relationships for predominant tree type over Østerild test station (see

Appendix A). Figure 4 show horizontal distribution of rounded heights of trees and PAI. Figure 5

shows the PAD profiles derived using allometric relationships that now can be used for

derivation of aerodynamic parameters.

CFD simulations using the full description of canopy drag forces (Figs. 6 and 7: Canopy drag)

and simulations using the effective roughness (Figs. 6 and 7: z0,eff) indicate that the major

difference is observed in the near-surface layer. The height of this layer depend on the vertical

structure of vegetation and can be varied from 20 m (about 2h - when z0,eff/h > 0.1) until 200 m

13

(about 10h - when z0,eff/h < 0.04) (see also Fig. 9). Above this height, the ABL wind profiles

derived by the different methods converge. Local friction velocities are also identical, except in

the canopy layer. The logarithmic ‘deflected’ profile of wind speed is in a good accordance with

the full canopy drag solution only in a very shallow layer near the canopy top. For the purposes

of wind energy, it is quite clear that the solution based on the new CFD method of determining

z0,eff is preferable. Figure 8 shows horizontal distribution of effective roughness over

investigated area. The roughness was derived for trees with PAD presented in Fig. 5. Referring

to data presented in Fig. 4b one can see that the area of higher LAI has lower roughness due to

forest architecture based on allometric relationships.

Figure 4. Horizontal distribution of rounded heights of tree h (m) (a) and PAI (m2 m-2) (b).

14

Figure 5. PAD profiles for trees of different height derived using allometric relationships for

Scots Pine (see Appendix A). Blue and red lines indicate the profile for tree heights of 10 m and

20 m, respectively

 

Figure 6. Wind speed (a

and c) and the dynamic

friction velocity (b and d) in

ABL (upper panels) and in

the surface layer (bottom

panels) modelled by

SCADIS using canopy drag

(black lines) and effective

roughness (red lines) for

forest height h = 10 m (G =

10 m s-1) (indicated in Fig.

5 by blue line). Logarithmic

displaced wind profiles

(blue lines) based on d and

z0 derived from SCADIS

with the canopy drag is

also shown (a and c).

Shaded areas indicate

canopy. The levels of d + z0

and z0,eff where the wind

speed takes zero value are

shown in (c). 

15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 7. The same as in

Fig. 6 except for forest

height h = 20 m (indicated

in Fig. 5 by red line).  

Figure 8. Horizontal distribution of effective roughness z0,eff (m).

16

Results of the sensitivity test with different shapes of PAD show that the effective roughness,

i.e. dynamical resistance of the underlying surface, depends on the vertical foliage distribution

for given h and PAI (Fig. 9). When foliage is mostly located in the lower or in the middle part of a

tree (α < 5) (for shape see Fig. 1) the roughness is growing with increase in the tree height, or

with growing PAI. When foliage is located in the upper part (α > 5) behaviour of the effective

roughness depending on the tree height and PAI becomes more unpredictable. For our case

with PADs presented in Fig. 5 the effective roughness grows with increase in the tree height

until tree height of 8 m, after that gradually decreases and reaches approximately a constant

value (z0,eff ≈ 0.7 m) for trees higher than 15 m. The sensitivity test shows that the knowledge

about the real vertical foliage profile is very important for correct estimation of aerodynamic

properties of vegetation.

Figure 9. Effect of different assumption about PAD on effective roughness. Blue line for z0,eff

derived using PAD profiles based on allometric relationships (see Fig. 5). Black lines for z0,eff

derived using PAD profiles described by Eq. (2) with varied α and fixed β at β = 3 (see Fig. 1). In

all cases the same class of tree height has the same PAI.

The goal of the present work is not to estimate real surface properties over investigated area

but to demonstrate the method of PAD translation into the effective roughness. PAD derived

from allometric relationships provide an effective roughness range over the area until 1.5 m

(Fig. 8). To provide a more clear effect of the effective roughness on the airflow modelling it will

be desirable to have a wider range of this parameter. At the same time the vertical shape of a

tree should still be close to the realistic one. The compromise here can be the choice of the tree

shape with zm/h = 0.5 and α = 3 (see Fig. 1 for the PAD shape).

17

The horizontal distribution of the effective roughness over a limited domain with new derived

PAD is given in Fig. 10a. The domain shown presents the most forested part of the initial area

and has minor variation in topography. Using this domain size of about 7 km x 7 km in modelling

allows us to consider only the effect of different forest representations on the airflow. For

modelling purposes forest height gradually decreases to zero at borders of the domain. Those

buffer zones are 500 m wide. This also implies that the effective roughness gradually attain the

roughness value for plane ground (z0 = 0.03 m) at the domain borders. Considering the limited

domain allows us also to better visualise how the effective roughness varies in space. For some

application the high variability of the parameter can be improper, and then we advise to apply

the bilateral filter (Section 3.3) for smoothing the parameters over the considered area. An

example of such filtering is given in Fig. 10b. One can see that small details are smoothed out,

but the ‘big picture’ (primary features) are still captured (e.g. in comparison to figure 10a).

Figure 10. The effective aerodynamic roughness length, z0,eff (m) estimated for a limited area

(a). The results of application of bilateral filter to original z0,eff with σs = 50 m and σr = 0.5 m is

also shown in (b) (see text for details).

18

6.2 Effect of different levels of canopy drag-force prescription on flow

modelling 6.2.1 Initialization

As mentioned above, in order to explore the effect of different levels of canopy drag-force

prescription on air flow modelling over forested terrain we consider a limited domain with flat

topography. Detailed views of space distribution of tree heights and PAI are given in Fig. 11a

and in Fig. 11b, respectively. As mentioned above, for airflow modelling with full implementation

of canopy drag the PAD profiles given by Eq. (2) with α = 3 and β = 3 were used. A roughness

of forest floor was set to 0.1 m. For airflow modelling based on a single parameter the effective

roughness given in Fig. 10a was used. Simulations using Ellipsys3D solver were performed

using the horizontal resolution of 16 m, while SCADIS simulations were performed using the

horizontal resolution of 48 m.

Figure 11. The vegetation height, h (m) (a) and plant area index, PAI (m2 m-2) (b) in a limited

domain used for airflow modelling.

19

6.2.2 Wind speed simulations

The results of the numerical experiments presented in Figs. 12, 13 and 14 show that both

models with different parameterization of the vegetation effect produce similar wind speeds over

the investigated domain. Effects of vegetation on the flow are clearly seen. When using the

canopy drag parameterization, both models, especially EllipSys3D (Figs. 12 and 13), provide

more details on wind speed at the height of 25 m, but with increasing the height wind speed

becomes smoothed. When using the effective roughness, both models provide smoothed wind

speed at all levels considered in the analysis. Some differences in results between the two

models do however exist (for further elaboration of this issue see Sogachev et al. 2015). Here

we focus on how each specific model copes with air flow modelling using different vegetation

representation.

The scatter plot in Fig. 15 shows that the CFD solution based on z0,eff is not applicable at low

elevations for both models. Wider scatter in resulted data for EllipSys3D (both with k - ω and

k - ε closures) can be due to higher canopy resolution used in this model and as such due to

introduction of more details in the calculations. Also it can be explained by different numerical

methods applied in SCADIS and EllipSys3D. With increase in height, the difference in wind

speed derived using different parametrizations becomes smaller, and scatter points increasingly

converge towards the 1 : 1 line (see Fig. 15), except for EllipSys3D based on k - ε closure. Wind

speed derived using the z0eff-approach is always higher than that derived using the full canopy

drag implementation. Besides general differences in the results due to different closures

(Sogachev et al. 2015), this result can indicate a possible problem of correct estimation of z0,eff

for this type of closures. Note that results demonstrated by SCADIS (smaller scatter) are in

better agreement than results of EllipSys3D solver. The reason of that can be that derivation of

z0,eff have been done based on SCADIS solution itself. Some other reasons will be discussed

later (see Section 7).

Figure 16 show the wind speed estimated by SCADIS along the west-east transect over the

area indicated in Fig.12 (dashed lines). One can see that the large difference in estimated wind

speed fields is observed in lowest layer of atmosphere and of course inside the layer occupied

by vegetation. With increase the height (z), the difference becomes smaller and at some height

the solutions of two models match each other.

20

Figure 12 . Wind velocity ( m s-1) at different heights modelled by SCADIS using the canopy

drag (on the left side) and the effective roughness ( on the right side). Dashed lines in the upper

panel indicate transects, the results of modelling along which presented in Fig.16.

21

Figure 13. Wind velocity ( m s-1) at different heights modelled by EllipSys3D (k - ω closure)

using the canopy drag (on the left side) and the effective roughness ( on the right side).

22

Figure 14. Wind velocity ( m s-1) at different heights modelled by EllipSys3D (k - ε closure)

using the canopy drag (on the left side) and the effective roughness ( on the right side).

23

Figure 15. Wind speed at 25 m AGL (grey), at 50 m AGL (blue) and at 100 m AGL (red) derived

by different models with canopy drag against that derived by models with the effective

roughness over the modelling domain. The 1 : 1 line is also shown.

Figure 16. Wind velocity (m s-1) along the west-east transect (see location in Fig. 12) modelled

by SCADIS using the canopy drag (left panel) and the effective roughness (right panel).

24

6.2.3 TKE simulations

Results for turbulent kinetic energy (TKE) resolved by using two modelling approaches for

vegetation show also a reasonable agreement between the two models (Figs. 17, 18 and 19).

Both models seem to describe the effect of vegetation on turbulence in a similar way, even

though some differences in absolute values of calculated TKE can be seen (especially for

EllipSys3D based on k - ε closure). One can observe indeed, that the forest increases

turbulence intensity. The areas of high values of TKE are located just above the forest and

spread downwind with the increasing height. The areas with denser and higher forest (see also

Figs. 10 and 11) indicate the larger effect on the TKE production. The scatter plot of TKE data

(Fig. 20) also shows that with height, the difference in turbulence levels calculated utilizing two

different approaches in the two models becomes a minor one. As in a case of the wind speed,

again the SCADIS results demonstrate a smaller scatter. Ellipsys3D (k - ε) results demonstrate

that besides larger scatter, the TKE estimated by this model using effective roughness

approach is smaller than TKE estimated using canopy drag approach. Reasons for that and

possible ways of improvement will also be discussed below.

As a whole, the results of numerical experiments show that CFD approach based on z0,eff

vegetation representation can do good work in estimation of air flow speed and turbulence level

over forested area at heights potentially interesting for wind industry applications (100 m and

higher).

25

Figure 17. Turbulent kinetic energy (m2 s-2) at different heights above the ground modelled by

SCADIS using the canopy drag (on the left side) and the effective roughness (on the right side).

26

Figure 18. Turbulent kinetic energy (m2 s-2) at different heights above the ground modelled by

EllipSys3D (k - ω closure) using the canopy drag (on the left side) and the effective roughness

(on the right side).

27

Figure 19. Turbulent kinetic energy (m2 s-2) at different heights above the ground modelled by

EllipSys3D (k - ε closure) using the canopy drag (on the left side) and the effective roughness

(on the right side).

28

Figure 20. TKE at 25 m AGL (grey), at 50 m AGL (blue) and at 100 m AGL (red) derived by

different models with canopy drag against that derived by models with the effective roughness

over the modelling domain. The 1 : 1 line is also shown.

7. Discussion

There are several issues that should be addressed and further tested, in order to assess how

well the presented simplified canopy description describes flow over forested areas. In the

following we outline some of the primary issues.

Forest data. Though we test the approach using simplified representation of real forested

terrain, the approach is applicable for initial information about vegetation of any complexity. For

example, the growing interest in LiDAR scans seems to promise finer resolution and improved

post-processing algorithms, which will eventually provide a better description of the forest

structure, and consequently better output from our approach. Having high-resolution information

from LiDAR scans allows for classification of data with any height graduation. Decreasing the

number of classes increases the number of PAD profiles in each class, effectively smoothing

the resultant profiles. It should be kept in mind that sparse but high vegetation types, which are

typical for clear-cuts, roads or power lines can produce unrealistic high values of the effective

roughness. The solution can be to separate, behind height classes, vegetation into two PAI

groups to correctly keep areas with low PAI. We also advise to test different thresholds of PAI

and tree height for which a given vegetation class can be replaced by an open-place class.

Empirical methodology. Two methods have been widely used for the representation of PAD

with minimum information about the tree structure. For dense and high forest the methods

provide similar shapes of vertical PAD (see Fig. 1) that will probably cause only minor

differences in resulting wind profiles. One advantage of the method based on the beta

probability (Meyers and Paw U, 1986) is, that for any set of non-negative α and β parameters,

the real plant area density depends only on the information about PAI. The method proposed by

Lalic and Michailovic (2004) needs information about PADm to get profiles and must be

corrected to provide the PAI needed.

29

Reduced-dimensionality and consistency with geostrophic drag law. Because the SCADIS

model has been validated extensively against different types of vegetation (e.g. Sogachev and

Panferov, 2006), we do not anticipate issues with its representation of basic flow statistics inside

the canopy. A minor unresolved issue is the choice of geostrophic drag-law coefficients A and B

used in equations (6) and (7). Both values are within the ranges given in the literature, with B

being slightly higher than typically-used values. The advanced turbulence model implementation

in SCADIS can be adjusted to satisfy classical B values, but without conducting comprehensive

tests, it is difficult to say whether the model will still reproduce canopy flow correctly. Here for

simplicity we use fitted values that provide a match of the SCADIS simulations with the vertically

distributed canopy drag, and only with z0,eff defined from equation 7 (see Figs. 6 and 7). Also, it

is important to note that the resultant z0,eff is a function of the wind speed; this is a feature

resulting from inclusion of the Coriolis force (among other things). Thus application of derived

z0,eff to different wind conditions at given site will also be tested. Further, the aggregate drag and

apparent geostrophic-scale roughness should be consistent, regardless of the number of

dimensions of the simulation (at least for homogeneous forest statistics).

CFD flow modelling. There is still a need for more numerical experiments to test the

sensitivity of flow modelling to different distributions of z0,eff ,also including topographical effects.

One of possible solution to get quick estimates of flow over forested terrain is application of a

mass-consistent model (e.g. Sherman 1978). The first guess about wind distribution can be

done based one estimation of ABL profiles from reduced-dimension CFD, which can be also

combined in lower part of ABL with log-law profile based on estimates of d and z0. There are

problems with the k - ε closure, relative to the k - ω; to estimate the better results we need to

use EllipSys3D with extra diffusion term (following Sogachev et al., 2012; 2015). There is also

another possibility, to estimate effective roughness using a one-dimensional k - ε model. There

are questions about how different closures behave regarding the effective roughness. Sogachev

et al (2012) showed that k - ω and k - ε in classical forms provide different results in canopy flow

modelling. Thus it should be also difference if we replace the canopy by effective roughness,

maybe the difference will be more pronounced and this happened in present study.

Filtering and smoothing data. To get a distribution of classes with resolution coarser than

that given by initial PAD data and especially in the case of fine LiDAR scan data, two options do

exist. Option 1 would be to use aggregated PAD values inside the coarse cell. Option 2 would

be to use classes derived on a small-resolution grid. A simple aggregation of classes inside

larger cell is incorrect, but we can aggregate dynamical properties of classes such as effective

roughness, displacement height or aerodynamic roughness. Aggregated values of effective

roughness can be used on finer grids directly, but do not allow us to identify vegetation classes.

Using the information about the aggregated displacement height and subgrid roughness

variation (within cells) helps, because these two parameters, in contrast to z0,eff, are unique for

each class.

30

8. Conclusions

We present a CFD method to facilitate use of forest data of any level of detail in flow models

with different types or levels of canopy drag-force prescription. Preliminary numerical tests

showed that CFD models with different levels of canopy drag-force prescription provide similar

results on both wind field and TKE level beginning from the some height over ground surface

(z/h > 3-5). The method also allows for consistent comparison with known theory,

measurements, and commonly-used parameters in forest-flow modelling. The spatial

information about effective roughness can be used as input, not only for CFD models, but also

for mesoscale or linearized models. In order to easily use the derived information in such

models, we suggest applying a bilateral filter (e.g. Tomasi and Manduchi, 1998) for smoothing

the parameters over the area considered; smoothing of aerodynamic parameters is more

physically-based than smoothing of discrete land-use classes.

31

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33

Appendix A Allometric relationships for Scots Pine

The plantation surrounding Østerild area today consists mainly of Scotch pine, mountain pine,

silver fir, sitka spruce and common spruce with smaller areas of beech, oak and birch. Also

many varieties of dwarf shrubs can be found such as bog bilberry, crowberry, heather, bell

heather and bog myrtle (http://green.thisted.dk). For simplicity we accept assumption that all

trees at the site are Scots Pines and to produce the information needed for modelling such as

PAD we apply some allometric equations describing tree architectural properties for Scots pine

(Pinus sylvestrics) ( see Widlowski et al., 2003). The DBH (Diameter-at-Breast-Height)

parameter is commonly expressed in units of centimetres [cm], whereas most of the

allometrically derived quantities retain their SI units, i.e., they are expressed in units of metres

[m]. Given review of existing allometric relationships for Scots pine, Widlowski et al., 2003

recommended the next expressions for the total tree height, h (Siipilehto, 2000)

2

1.3 m0.894 0.185

DBHh

DBH

, (A.1)

and PAI (Cermák et al., 1998)

0.375PAI exp(0.375)DBH . (A.2)

Having as input information about h we can estimate DBH and after that PAI as a function of

tree height. The problem of expression (A.1) that h arrives the upper tree height limit around 26

m that will give a very large PAI values, for trees higher than 20 m. We suggest a simplified

expression for PAI as function of h

PAI 5 30mh . (A.3)

Eq. (A.3) is in a good agreement with Eqs. (A.1) and (A.2) for tree height till 20 m and provides

also reasonable solution for higher heights (see Fig. 21).

34

Figure 21. The Plant Area Index ( PAI ) for Scots pine when derived from the allometric

relationships (A.1) and (A.2) and the simplified expression (A.3) as function of the tree height.

Eq. (A.3) provides also a good agreement with experimental data about PAI for a forested

region near Ryningsnäs in the south-east of Sweden located approximately at the same latitude

as Østerild. According to Arnqvist et al. (2015) the forest is consisted predominantly of Scots

pine (Pinus silvestris) and the average forest height is approximately 20 m. Nebenführ and

Davidson (2015) successfully modelled wind flow over this area with PAI = 4.3.

The heights (zm) where maximum plant area density PADm occurs is a cruisial parameter in

derivation of PAD profile. Pretzsch et al. (2002) indicates that the height to the maximum crown

width for Scots pine can be approximated by zm = 0.5(h+ht), where ht is the height to the tree

crown, given as

0.376 0.9963 0.0218

* 1 exp mh

DBHDBH

th h

. (A.4)

However, Widlowski et al. (2003) pointed out that this allometric formulation makes that ht is

almost equal to the tree height h at low DBH values thus almost completely eliminating the

crown length. To account for the fact that the crown of young trees often extends almost to the

ground, Cermák et al. (1998) provided the following relationship

9.513

** 3.4516.9 1 exp mDBH

th

. (A.5)

35

As it seen this realtionship has a upper limit for the crown height. As solution we used the

geometrical mean of this two expression. Thus the normalized height with maximul PAD value

was derived as

* **1

2 2t tm

h hz

h

, (A.6)

where h is given by Eq. (A.1). The behaviour of this function as function of h is shown in Fig. 22.

Assuming that after achieving its maximum the value zm/h does not change we parameterize the

behaviour of zm/h by the sigmoidal five parameters equation

1.2872

0.3980.4922

1 exp 8.5174 2.5499

mz

h h

, (A.7)

which is also presented in Fig. 22.

Figure 22. The normalized heights of maximal values of PAD derived by using different

allometric relationships and using the empirical fit.

The expression (A.7) can be directly applicable in Eq. (4) for estimation of α under some

assumption of values β (usually accepted as 3). Together with Eq. (A.3) that further provides

PAD profile simply as function of h from Eq. (2). Using of Eq. (6) is still difficult so far as no

information about values of PADm is known.

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